AP Calculus AB/BC Academy™
DERIVATIVES CALCULUS™
From Instantaneous Rate of Change to Advanced Differentiation™
Build derivatives from first principles through graphical, numerical, symbolic, analytical, and AP-style representations.
Representations:GraphicalNumericalSymbolicAnalyticalAP-Style
12
Lesson Modules
48
Practice Sets
20
AP FRQ Drills
5
Mastery Targets
Learning Progression
Derivatives Mastery Roadmap™
Trace the path from the limit concept to applied differentiation mastery.
01Limit
02Average Rate of Change
03Secant Line
04Δx → 0
05Instantaneous Rate of Change
06Tangent Line
07Derivative
08Derivative Function
09Differentiation Rules
10Applications
1
Understand Change
Begin with average rates and the intuition of motion.
2
Build the Difference Quotient
Construct the secant slope and the symbolic quotient.
3
Take the Limit
Let Δx → 0 to pass from secant to instantaneous change.
4
Interpret the Derivative
Read the tangent line and the derivative as a function.
5
Master Differentiation Rules
Apply the product, quotient, and chain rules fluently.
6
Apply Derivatives
Solve motion, optimization, and AP-style analysis problems.
Representational Philosophy
Numerical↔Graphical↔Symbolic↔Analytical↔AP Application
Table of Contents
Derivatives Curriculum
Four units · twenty-two modules from first principles to AP mastery.